The Steinhaus theorem for Toeplitz matrices in non-archimedean fields
The article contains no abstract
New properties of the Natarajan method of summability
The method of summability was introduced in 2013 by Natarajan. In the paper some new properties of this method are studied.
Steinhaus Type Theorems for Summable Sequences
In this short paper, entries of infinite matrices and sequences are real or complex numbers. We prove a few Steinhaus type theorems for summable sequences.
A New Definition of Convergence of a Double Sequence and a Double Series and Silverman-Toeplitz Theorem
Throughout this paper, entries of 4-dimensional infinite matrices, double sequences and double series are real or complex numbers. In the present paper, we introduce a new definition of convergence of a double sequence and a double series and record a few results on convergent double sequences. We also prove Silverman-Toeplitz theorem for double sequences and series.
Some Characterizations of Schur Matrices in Ultrametric Fields
In this short paper, denotes a complete, non-trivially valued, ultrametric field. Sequences and infinite matrices have entries in K. We prove a few characterizations of Schur matrices in . We then deduce some non-inclusion theorems modelled on the results of Agnew [1] and Fridy [3] in the classical case.
Another Theorem on Weighted Means
In this short paper, which is a continuation of [2], we prove another interesting result concerning weighted means.
Cauchy Multiplication of Euler Summable Series in Ultrametric Fields
Euler summability method in a complete, non-trivially valued, ultrametric field of the characteristic zero was introduced by Natarajan in [7]. Some properties of the Euler summability method in such fields were studied in [2] and [7]. The purpose of the present note is to continue the study and to prove a pair of theorems on the Cauchy product of Euler summable sequences and series.
Page 1